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Multiscale Stochastic Volatility with the Hull–White Rate of Interest

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  • Jeong‐Hoon Kim
  • Ji‐Hun Yoon
  • Seok‐Hyon Yu

Abstract

Although interest rates fluctuate randomly, many option‐pricing models do not fully take into account their stochastic nature because of their generally limited impact on option prices. However, stochastic changes in stochastic interest rates may exert a significant impact on option prices when issues of maturity, hedging, or stochastic volatility are considered. This study incorporates the term structure of a stochastic interest rate driven by a Hull–White process into a stochastic volatility model in order to assess the sensitivity of option prices to changes in interest rate. It demonstrates that a stochastic volatility model with a stochastic interest rate outperforms a model with a constant interest rate, particularly, for short time‐to‐maturity European options. © 2013 Wiley Periodicals, Inc. Jrl Fut Mark 34:819–837, 2014

Suggested Citation

  • Jeong‐Hoon Kim & Ji‐Hun Yoon & Seok‐Hyon Yu, 2014. "Multiscale Stochastic Volatility with the Hull–White Rate of Interest," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(9), pages 819-837, September.
    • Handle: RePEc:wly:jfutmk:v:34:y:2014:i:9:p:819-837
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    Cited by:

    1. Lin, Sha & He, Xin-Jiang, 2020. "Pricing variance and volatility swaps with stochastic volatility, stochastic interest rate and regime switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    2. Ben-zhang Yang & Jia Yue & Nan-jing Huang, 2017. "Variance swaps under L\'{e}vy process with stochastic volatility and stochastic interest rate in incomplete markets," Papers 1712.10105, arXiv.org, revised Mar 2018.
    3. Cao, Jiling & Lian, Guanghua & Roslan, Teh Raihana Nazirah, 2016. "Pricing variance swaps under stochastic volatility and stochastic interest rate," Applied Mathematics and Computation, Elsevier, vol. 277(C), pages 72-81.
    4. Yoon, Ji-Hun, 2015. "Pricing perpetual American options under multiscale stochastic elasticity of variance," Chaos, Solitons & Fractals, Elsevier, vol. 70(C), pages 14-26.
    5. Teh Raihana Nazirah Roslan & Wenjun Zhang & Jiling Cao, 2016. "Pricing variance swaps with stochastic volatility and stochastic interest rate under full correlation structure," Papers 1610.09714, arXiv.org, revised Apr 2020.
    6. Ben-Zhang Yang & Jia Yue & Nan-Jing Huang, 2019. "Equilibrium Price Of Variance Swaps Under Stochastic Volatility With Lévy Jumps And Stochastic Interest Rate," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(04), pages 1-33, June.

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